U.S. patent application number 14/241309 was filed with the patent office on 2014-08-07 for method for controlling interference from white space units.
This patent application is currently assigned to Telefonaktiebolaget L M Ericsson (publ). The applicant listed for this patent is Jonas Kronander, Yngve Selen. Invention is credited to Jonas Kronander, Yngve Selen.
Application Number | 20140220901 14/241309 |
Document ID | / |
Family ID | 45373831 |
Filed Date | 2014-08-07 |
United States Patent
Application |
20140220901 |
Kind Code |
A1 |
Selen; Yngve ; et
al. |
August 7, 2014 |
Method for Controlling Interference from White Space Units
Abstract
The present invention relates to a method of a node such as a
geo-location database, for controlling an aggregated interference
generated by at least two white space units in at least one point
in space for at least one frequency channel. A model of propagation
channels from each of the at least two white space units to each of
the at least one point comprises a variable with a lognormal
distribution. The method comprises receiving (810) requests for
usage of white space frequency channels from the at least two white
space units, the requests comprising positions of the at least two
white space units. The method also comprises determining (820)
output power limits for the at least two white space units by
maximizing a utility function while fulfilling a probabilistic
constraint on the amount of aggregated interference generated in
each of the at least one point, based on the received requests and
on said model of propagation channels. A sum of lognormal variables
in the probabilistic constraint is approximated by a single
lognormal variable. The method further comprises transmitting (830)
the determined output power limits to the respective at least two
white space units.
Inventors: |
Selen; Yngve; (Uppsala,
SE) ; Kronander; Jonas; (Knivsta, SE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Selen; Yngve
Kronander; Jonas |
Uppsala
Knivsta |
|
SE
SE |
|
|
Assignee: |
Telefonaktiebolaget L M Ericsson
(publ)
Stockholm
SE
|
Family ID: |
45373831 |
Appl. No.: |
14/241309 |
Filed: |
November 8, 2011 |
PCT Filed: |
November 8, 2011 |
PCT NO: |
PCT/SE2011/051339 |
371 Date: |
February 26, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61529501 |
Aug 31, 2011 |
|
|
|
Current U.S.
Class: |
455/63.1 |
Current CPC
Class: |
H04B 17/391 20150115;
H04W 52/225 20130101; H04W 52/367 20130101; H04W 16/14 20130101;
H04B 15/00 20130101 |
Class at
Publication: |
455/63.1 |
International
Class: |
H04B 15/00 20060101
H04B015/00; H04W 16/14 20060101 H04W016/14 |
Claims
1-25. (canceled)
26. A method of a node, for controlling an aggregated interference
generated by at least two white space units in at least one point
in space for at least one frequency channel, Wherein a model of
propagation channels from each of the at least two white space
units to each of the at least one point comprises a variable with a
lognormal distribution, the method comprising: receiving requests
fir usage of white space frequency channels from the at least two
white space units, the requests comprising positions of the at
least two white space units, determining output power limits for
the at least two white space units by maximizing a utility function
while fulfilling a probabilistic constraint on the amount of
aggregated interference generated in each of the at least one
point, based on the received requests and on said model of
propagation channels, wherein a sum of lognormal variables in the
probabilistic constraint is approximated by a single lognormal
variable, and transmitting the determined output power limits to
the respective at least two white space units.
27. The method according to claim 26, further comprising: checking
by means of a Monte-Carlo, MC, simulation if the determined output
power limits fulfil the probability constraint, and transmitting
the determined output power limits to the respective at least two
white space units if the determined output power limits fulfil the
probability constraint.
28. The method according to claim 26, wherein the utility function
is one of: a sum-capacity; a sum-power; or a total throughput.
29. The method according to claim 26, wherein the probabilistic
constraint corresponds to a probability that each of the at least
one points has an aggregated interference which exceeds an
interference value threshold, wherein the probability is
constrained to be below a probability threshold.
30. The method according to claim 26, wherein Fenton-Wilkinson
approximation is used for approximating the sum of lognormal
variables by a single lognormal variable.
31. The method according to claim 26, wherein the determining of
output power limits is subject to an additional constraint that the
determined output power limits must be equal to or lower than a
maximum output power value.
32. The method according to claim 31, wherein the maximum output
power value is received in at least one of the requests, is
pre-defined, or is determined based on capabilities of the at least
two white space units.
33. The method according to claim 26, wherein the determining of
output power limits is subject to an additional constraint that the
determined output power limits must be the same for all of the at
least two white space units.
34. The method according to claim 26, further comprising: comparing
at least one of the determined output power limits with a minimum
output power value related to a corresponding white space unit, and
if the at least one of the determined output power limits is below
the minimum output power value: determining the output power limits
again with at least one of the at least two white space units
removed.
35. The method according to claim 34, wherein the minimum output
power value is received in at least one of the requests.
36. The method according to claim 26, wherein the aggregated
interference is controlled in at least two frequency channels, and
wherein the model of propagation channels for the at least two
frequency channels takes adjacent channel suppression into
account.
37. The method according to claim 26, wherein the maximizing of the
utility function comprises a selection of at least one of several
frequency channels for each of the at least two white space
units.
38. The method according to claim 37, wherein the determining of
output power limits is subject to at least one of the following
constraints: a constraint on a number of simultaneously used
frequency channels for the at least two white space units; a
constraint on a total transmit power for each of the at least two
white space units over all selected frequency channels; a
constraint that the at least two white space units must use
contiguous frequency channels.
39. The method according to claim 26, wherein each of the at least
two white space units is a white space device, or a white space
system.
40. The method according to claim 26, wherein the node is a
geo-location database.
41. A node configured to control an aggregated interference
generated by at least two white space units in at least one point
in space for at least one frequency channel, wherein a model of
propagation channels from each of the at least two white space
units to each of the at least one point comprises a variable with a
lognormal distribution, the node comprising a communication unit
and a processing unit, wherein the communication unit is configured
to receive requests for usage of white space frequency channels
from the at least two white space units, the requests comprising
positions of the at least two white space units, the processing
unit is configured to determine output power limits for the at
least two white space units by maximizing a utility function while
fulfilling a probabilistic constraint on the amount of aggregated
interference generated in each of the at least one point, based on
the received requests and on said model of propagation channels,
wherein a sum of lognormal variables in the probabilistic
constraint is approximated by a single lognormal variable, and the
communication unit is further configured to transmit the determined
output power limits to the respective at least two white space
units.
42. The node according to claim 41, wherein the processing unit is
further configured to check by means of a Monte-Carlo, MC,
simulation if the determined output power limits fulfil the
probability constraint, and the communication unit is further
configured to transmit the determined output power limits to the
respective at least two white space units if the determined output
power limits fulfil the probability constraint.
43. The node according to claim 41, wherein the processing unit is
configured to approximate the sum of lognormal variables by a
single lognormal variable by using a Fenton-Wilkinson
approximation.
44. The node according to claim 41, wherein the processing unit is
configured to determine output power limits subject to an
additional constraint that the determined output power limits must
be equal to or lower than a maximum output power value.
45. The node according to claim 41, wherein the processing unit is
configured to determine output power limits subject to an
additional constraint that the determined output power limits must
be the same for all of the at least two white space units.
46. The node according to claim 41, wherein the processing unit is
further configured to: compare at least one of the determined
output power limits with a minimum output power value related to a
corresponding white space unit, and if the at least one of the
determined output power limits is below the minimum output power
value: determine the output power limits again with at least one of
the at least two white space units removed.
47. The node according to claim 46, wherein the communicating unit
is configured to receive the minimum output power value in at least
one of the requests.
48. The node according to claim 41, wherein the maximizing of the
utility function comprises a selection of at least one of several
frequency channels for each of the at least two white space
units.
49. The node according to claim 48, wherein the processing unit is
configured to determine output power limits subject to at least one
of the following constraints: a constraint on a number of
simultaneously used frequency channels for the at least two white
space units; a constraint on a total transmit power for each of the
at least two white space units over all selected frequency
channels; a constraint that the at least two white space units must
use contiguous frequency channels.
50. The node according to claim 41, wherein the node is a
geo-location database.
Description
TECHNICAL FIELD
[0001] The disclosure relates to the field of determining output
power limits for white space devices. More particularly, the
disclosure relates to a node, and a method in the node for
controlling an aggregated interference generated by at least two
white space units in at least one point in space for at least one
frequency channel.
BACKGROUND
[0002] Spectrum scarcity is a problem that has been observed in
regulative frequency allocation charts for some time. All
potentially interesting spectrum bands for mobile communication are
already allocated to services. However, additional spectrum for
mobile broadband is needed to cope with the exponential take-off of
mobile broadband traffic. At the same time traditional spectrum
regulatory methods are sometimes perceived as too slow to adapt to
the sometimes rapidly changing economic and technical requirements,
implying that large parts of the electromagnetic spectrum is
licensed but not effectively used.
[0003] In particular, the TV broadcast spectrum is not efficiently
used due to the way the TV broadcast networks have been deployed.
They are based on the concept of high transmit towers with high
transmit power serving large areas with digital or analog TV. This
type of deployment makes the frequency reuse distance large--in the
order of 100 km--implying a spatially sparse use of the frequency
band. The geographical areas where a TV frequency channel is not in
use have been termed TV white space for that channel.
[0004] Motivated by the underutilization of e.g. the TV broadcast
bands, the research community has during the last decade performed
research into so called secondary spectrum access. The goal of
secondary spectrum access is to use licensed but unused parts of
the spectrum, e.g. the TV broadcast bands, for communication in
such a way that a primary user, i.e., the user of the service
provided by the license holder or the one having prioritized right
to use the spectrum, is not negatively affected by the
transmissions in the secondary system.
[0005] The central idea behind secondary spectrum access by
secondary systems is thus to use already licensed or allocated
spectrum for secondary purposes, i.e., for communication between a
secondary transmitter and a secondary receiver or two secondary
transceivers. As an example, the TV white spaces in the TV
broadcast spectrum could be used for secondary purposes. Secondary
users in a secondary system may also be referred to as a white
space devices (WSD) in a white space system, which are thus units
that opportunistically use spectrum licensed or dedicated for a
primary service on a secondary basis at times or locations where a
primary user is not using the spectrum. As already mentioned above,
the WSD or white space systems are not allowed to cause harmful
interference to the primary service. Furthermore, the WSD and white
space systems are not protected from interference from any primary
service or user.
[0006] Recently, the United States (US) regulatory body Federal
Communications Commission (FCC) has opened up the opportunity for
secondary usage of the TV broadcast band in the US under a set of
conditions. Furthermore, the regulator authority Ofcom is well on
the progress of finalizing a rule set that allows secondary usage
of the TV broadcast bands in the United Kingdom (UK). In Europe,
the regulatory standardization group European Conference of Postal
and Telecommunications Administrations (CEPT) SE43 has lately
finalized a report outlining the requirements for operating as a
secondary user in the TV white spaces. Thus, the process of opening
up TV white spaces for secondary usage around the globe is well
under way.
[0007] One commonality to the rules in place in the US and the
proposed rules in Europe and UK is that one allowed way of
discovering spectrum opportunities for secondary usage to get
access to the TV white spaces, i.e., perform secondary
transmissions in the TV bands, is to access a centrally managed
database referred to as a geo-location database. Upon a query from
a secondary user or a WSD, the geo-location database provides the
WSD with a list of TV channels available for secondary usage, also
called TV white space channels, at the location of the WSD. The WSD
may provide information regarding its location and possibly also
additional information in the database query. Furthermore, in the
CEPT SE43 proposal, the WSD obtains maximum allowed transmit power
levels associated with the channels available for secondary usage
in the response from the database. These transmit power levels are
based on an estimation of how much interference that would be
generated in a worst case, including a margin to take into account
the aggregated interference from multiple WSDs using the same white
space spectrum.
[0008] The control of the aggregated interference towards a certain
point, line, area or volume is an important problem since
regulators enforce limits on the interference a system is allowed
to cause to other systems. Particularly for secondary usage of
spectrum, e.g., TV broadcast bands, it is of vital importance to
assure that the interference caused by multiple secondary users or
systems to a primary user does not exceed a threshold of harmful
interference, or at least exceeds the threshold only with a low
enough probability.
[0009] Setting an arbitrary margin to take aggregated interference
from multiple WSDs into account is not the most efficient way of
using the white space spectrum. A fixed margin cannot account for
the different types of interference which is caused from different
numbers of secondary users with different fading situations. There
is a risk of choosing a margin value which is either
overprotective, which would mean that the WSDs are not allowed to
use spectrum which could actually be used, or which does not
protect enough, which would mean that the WSDs would cause harmful
interference in many cases.
SUMMARY
[0010] An object is therefore to address some of the problems and
disadvantages outlined above, and to determine WSD output power
limits without having to assume a worst case scenario and a fixed
margin to account for interference from multiple WSDs, as this
solution results in a sub-optimal output power limit allocation for
the WSDs. This may be achieved by formulating an optimization
problem that may be efficiently solved to determine the output
power limits. The optimization problem should be based on a
maximizing of a sum-capacity or some other value measuring the
utility of the secondary users, subject to constraints on allowed
output power of the secondary users and a probabilistic constraint
on the amount of aggregated interference they are allowed to cause
to a primary user.
[0011] In accordance with a first aspect of embodiments, a method
of a node, for controlling an aggregated interference generated by
at least two white space units in at least one point in space for
at least one frequency channel is provided. A model of propagation
channels from each of the at least two white space units to each of
the at least one point comprises a variable with a lognormal
distribution. The method comprises receiving requests for usage of
white space frequency channels from the at least two white space
units, the requests comprising positions of the at least two white
space units. The method also comprises determining output power
limits for the at least two white space units by maximizing a
utility function while fulfilling a probabilistic constraint on the
amount of aggregated interference generated in each of the at least
one point, based on the received requests and on said model of
propagation channels. A sum of lognormal variables in the
probabilistic constraint is approximated by a single lognormal
variable. The method further comprises transmitting the determined
output power limits to the respective at least two white space
units.
[0012] In accordance with a second aspect of embodiments, a node
configured to control an aggregated interference generated by at
least two white space units in at least one point in space for at
least one frequency channel is provided. A model of propagation
channels from each of the at least two white space units to each of
the at least one point comprises a variable with a lognormal
distribution. The node comprises a communication unit and a
processing unit. The communication unit is configured to receive
requests for usage of white space frequency channels from the at
least two white space units, the requests comprising positions of
the at least two white space units. The processing unit is
configured to determine output power limits for the at least two
white space units by maximizing a utility function while fulfilling
a probabilistic constraint on the amount of aggregated interference
generated in each of the at least one point, based on the received
requests and on said model of propagation channels. A sum of
lognormal variables in the probabilistic constraint is approximated
by a single lognormal variable. The communication unit is further
configured to transmit the determined output power limits to the
respective at least two white space units.
[0013] An advantage of embodiments is that the output power limits
of the WSDs are adapted to the actual situation and the determining
of the output power limits does not rely on a fixed margin to take
aggregated interference into account. This allows for better and
more efficient white space utilization. Furthermore, the
approximation used to simplify the optimization problem offers good
performance in terms of speed and precision.
[0014] Other objects, advantages and novel features of embodiments
will be explained in the following detailed description when
considered in conjunction with the accompanying drawings and
claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 is a block diagram illustrating a primary and a
secondary system according to prior art.
[0016] FIG. 2 illustrates schematically worst case position
assumptions for secondary systems.
[0017] FIG. 3 is a diagram schematically illustrating an example
realization with five WSDs outside the protection contour of a DTV
system.
[0018] FIG. 4 is a diagram schematically illustrating median values
of the aggregated interference along the protection contour.
[0019] FIG. 5 is a diagram schematically illustrating the received
power for a Fenton-Wilkinson (FW) approximation compared to that
obtained by a Monte Carlo (MC) simulation.
[0020] FIGS. 6-7 are histograms illustrating the resulting
probabilities of harmful interference for two different fading
standard deviations.
[0021] FIGS. 8a and 8b are flowcharts illustrating the method of
the node according to embodiments.
[0022] FIGS. 9a-b are block diagrams illustrating the node
according to embodiments.
DETAILED DESCRIPTION
[0023] In the following, different aspects will be described in
more detail with references to certain embodiments and to
accompanying drawings. For purposes of explanation and not
limitation, specific details are set forth, such as particular
scenarios and techniques, in order to provide a thorough
understanding of the different embodiments. However, other
embodiments that depart from these specific details may also
exist.
[0024] Moreover, those skilled in the art will appreciate that
while the embodiments are primarily described in form of a method
and a device, they may also be embodied in a computer program
product as well as in a system comprising a computer processor and
a memory coupled to the processor, wherein the memory is encoded
with one or more programs that may perform the method steps
disclosed herein.
[0025] This disclosure describes a method and apparatus to
calculate and limit, i.e. to control, the level of aggregated
interference which is caused to a point, line, area, or volume
which should be protected. The method is typically run at a central
entity or node, e.g., a server controlled by a white space database
operator, to which WSDs send their requests for using spectrum. The
previously described geo-location database is one example of such a
central entity. The entity executing the method replies to the
requests from the WSDs, and provides upper output power limits that
may be used by the WSDs. These limits are typically valid for a
limited amount of time, after which a new optimization may be
made.
[0026] The technology applies both to the case when WSDs operate on
a single radio channel as well as to the case when the WSDs operate
on several channels. Further it applies to the case where the
primary receivers which need to be protected may be present on only
one or on several frequency channels, i.e., a constraint on the
aggregated interference is present for one or many channels.
Furthermore, WSD transmission leakage into neighboring channels is
also handled.
[0027] The disclosure comprises a formulation of an optimization
problem for optimizing a desired quantity, e.g., sum-capacity of
the secondary users subject to constraints on allowed output power
of the secondary users and a probabilistic constraint on the amount
of aggregated interference they are allowed to cause to a primary
user. The probabilistic constraint is infeasible to directly take
into account in a numerical solver so it may be replaced by a
highly computationally efficient approximation which also gives
good performance. This allows efficient solving of the optimization
problem, the solution of which thereafter may be checked by means
of a Monte Carlo (MC) simulation. If the solution of the
optimization problem is good enough compared to the MC simulation
it is accepted. If not good enough, the output of the optimization
problem may be used as a starting point for a further possibly more
complex optimization, or the solution may be given some simple
modification. A numerical evaluation of the proposed method is
given below to prove that it works well.
[0028] The disclosure may be summarized as follows:
[0029] The problem of finding the output power limits for WSDs is
described as a mathematical optimization problem. It is recognized
that a direct solution of the problem is computationally infeasible
due to a complicated constraint. Therefore, the complicated
constraint may be replaced by an approximation, resulting in a
simplified problem. An efficient approximation which further offers
good performance is found in the form of the Fenton-Wilkinson (FW)
approximation, which is one alternative embodiment. It is also
recognized that the solution of the simplified problem, while it
turns out to most likely fulfill the initial constraints, may
optionally be checked by means of a MC simulation. A variety of
options for the optimization problem is identified and described,
e.g., in the form of additional constraints, and in the form of
additions to consider interference on neighboring channels.
Furthermore, it is described what entities that communicate, what
kind of information is transferred between them, and at what type
of entity the simplified optimization problem is solved.
[0030] Embodiments are described herein by way of reference to
particular example scenarios. Particular aspects are described in a
non-limiting general context in relation to a primary TV broadcast
system and TV white space usage. It should though be noted that the
embodiments may also be applied to other types of primary systems
such as evolved LTE, Universal Mobile Telecommunications System
(UMTS), cdma2000, WiFi, distance measuring equipment for
aeronautical navigation purposes and radar systems.
[0031] A non-limiting example scenario is illustrated in FIG. 1,
where the secondary system or white space system 20 is an e-UTRAN,
comprising of evolved Node Bs (eNB) 100 with a service coverage
area 110. The UEs 150a-b are the WSDs within the service coverage
area 110 controlled or served by the eNBs. The eNB 100 is connected
to the geo-location database 160, typically via the Internet. The
primary system 10 is in this example scenario a TV broadcast system
providing a TV broadcast service to the primary TV receivers 170 in
a certain service area 130. However, in an alternative exemplary
embodiment the secondary system may be any other type of wireless
communication system supporting white space usage. Similarly, also
the primary system may be any other type of system, including radar
systems and aeronautical navigation systems.
[0032] The problem to be solved by the present disclosure is that
of finding upper power limits for radio transmitters for which the
aggregated interference they cause to a point, line segment or area
must be constrained. One example of a use case is that of secondary
transmitter operating near a Digital TV (DTV) service area. The
system controlling the output power of these secondary transmitters
must be able to guarantee, with a sufficiently high probability,
that the aggregated interference these secondary transmitters cause
to the DTV service area is below a certain threshold; i.e., such
that the risk of harmfully affecting a DTV receiver is low. For a
single transmitter e.g., a secondary transmitter, the upper power
limit may typically be computed according to the following:
p=argmaxp (1)
[0033] subject to the constraints
Pr{pG.gtoreq..tau.}].ltoreq..epsilon., and p.gtoreq.0. .tau. is a
critical interference value of a primary receiver, i.e., a value
that must not be exceeded, and .epsilon. is the
acceptable--typically low--probability that .tau. is exceeded. The
function Pr is used to denote "the probability of". Here, p is the
power level of the transmitter and G describes the path gain
including antenna gains and other effects. It will be assumed
herein, and it is often the case, that G is modeled as a lognormal
random variable due to the typical lognormal fading model.
[0034] From here on the example of secondary transmitters causing
aggregated interference to a primary system will be used in the
description. The term white space device (WSD) will also
interchangeably be used for the term secondary transmitter. It
should be realized that this is but one application area for the
problem and solution at hand. Also, in this text no technical
difference will be made between interference caused from secondary
systems and from individual secondary transmitters. Typically, the
worst case position assumption for a secondary system, which is a
single transmitter as close as possible to the protected region or
a receiver of the primary system, would be assumed. FIG. 2 shows an
example of a relevant scenario for the current technology. The
secondary service areas are the striped circles S.sub.1, S.sub.2,
S.sub.3, S.sub.N. A point at the edge of the circular service area
of the protected primary system P1 corresponding to an angle
.alpha. is illustrated with a dot and the worst case secondary
transmitter locations are illustrated as squares. The primary
service area P1 has a radius denoted R. The N secondary systems
have corresponding radii of service areas S.sub.1-S.sub.N denoted
r1-rN.
[0035] For the case of multiple secondary transmitters or systems
the problem becomes more complicated than in equation (1) above.
There are now multiple power limits to decide and the transmitters
compete for the total aggregated interference they are allowed to
cause in the sense that if the power limit for one secondary
transmitter or system is lowered, another transmitter or system may
be able to increase its power limit. Assuming N secondary
transmitters or systems the upper power limit may be computed
according to the following:
p=argmax.sub.pf(p) (2)
[0036] subject to the following constraints:
[max.sub..alpha.Pr{p.sup.TG(.alpha.).gtoreq..tau.}].ltoreq..epsilon.
(3)
p.sub.i.gtoreq.0,i=1, . . . ,N (4)
p.sub.i.ltoreq.p.sub.i.sup.max,i=1, . . . ,N (5)
[0037] Further constraints than the ones mentioned in (3)-(5) may
be added. An advantage of embodiments is that there is a
flexibility with regards to the choice of constraints on the power
limits that may be added to the probabilistic constraint in
(3).
[0038] The function f(p) is the quantity or utility function to
maximize, e.g., a sum-capacity or some other relevant measure. Some
examples of measures to maximize are given hereinafter. p=[p.sub.1
p.sub.2 . . . p.sub.N].sup.T is the power vector and p is the
optimal power limit allocation.
[0039] G(.alpha.)=[G.sub.1(.alpha.) G.sub.2(.alpha.) . . .
G.sub.N(.alpha.)].sup.T is the gain vector including pathloss,
antenna gains, and other effects, and the variable .alpha. is used
to denote that the aggregate interference constraint must be
fulfilled at one or multiple points, a line, an area or a volume.
.alpha., which may be a vector or a scalar, spans all these
possibilities in this expression. An example, illustrated in FIG.
2, in which .alpha. denotes an angle which uniquely describes a
point on a circular protection contour will be considered, e.g.,
for a primary DTV system. The first constraint (3) for equation (2)
hence guarantees that there is no point on the protection contour
that has a greater probability than .epsilon. of having an
aggregate interference from the N transmitters which exceeds the
value .tau.. The second (4) and third (5) constraints for equation
(2) constrain the output power of an individual secondary
transmitter to be within feasible levels. The maximum output power
value p.sub.i.sup.max may, e.g., be defined from the capabilities
of the secondary transmitter, or from regulatory requirements.
Alternatively the WSD may simply have no use of a higher power
level than this maximum output power value, and therefore transmits
this information to the entity performing the optimization.
[0040] As already mentioned, G.sub.i is typically lognormally
distributed, i.e.,
G.sub.i.about.LN(m.sub.Gi,.sigma..sub.Gi.sup.2), or
G.sub.i,dB.about.N(m.sub.Gi,dB,.sigma..sub.Gi,dB.sup.2). (6)
[0041] m.sub.Gi,dB is the mean and .sigma..sub.Gi,dB.sup.2 is the
variance of the normal distribution of G.sub.i,dB. The parameters
without dB in the subscript denote the corresponding quantities in
a linear scale, where m.sub.Gi denotes the median value of the
lognormal distribution. The further constraints which may be added
with equation (2) could, e.g., relate to fairness. A power fairness
constraint may e.g. be given by p=p.sub.eq[1 1 . . . 1].sup.T where
p.sub.eq is the power level equal for all transmitters. Fairness
may also be incorporated in the shape of the function f(p), where
the function could increase considerably when WSDs with a current
low capacity increase their power levels, and increase less when
WSDs with already high capacity further increase their power
levels.
[0042] The so called objective function or utility function f(p)
defines the quantity to optimize, which in the examples given here
are quantities to maximize. A natural function to maximize would
be, e.g., the sum-capacity of the WSDs or secondary systems. In
that case:
f ( p ) = B i = 1 N log 2 ( 1 + p i g i n i ) ( 7 )
##EQU00001##
[0043] where B is the bandwidth used by the secondary system, or
the channel bandwidth assuming that all secondary systems wish to
use this bandwidth. The equation may be generalized to different
bandwidths for different systems. g.sub.i is the intra-system gain,
i.e., within the secondary system i. G.sub.i, on the other hand,
denotes the inter-system gain from a secondary transmitter i to a
primary system. n.sub.i is the noise plus interference level for
secondary system i. The interference from one or more primary
systems may be taken into account such that n.sub.i is reduced when
the distance from the primary service areas increases. The
interference from the other WSDs or secondary systems may also be
included in n.sub.i. A possible formulation of n.sub.i would then
be:
n i = n Floor , i + g iP p p + j = 1 , j .noteq. i N .beta. j g ij
p j ( 8 ) ##EQU00002##
[0044] where n.sub.Floor,i is the residual noise floor at WSD i,
g.sub.iP is the channel gain, including antenna gain and other
effects, between the primary transmitter which has a transmit power
of p.sub.P and the WSD. If there are multiple primary transmitters
it is a sum of such channel gains. g.sub.ij is the gain between the
WSDs or systems i and j, and .beta..sub.j.ltoreq.1 is a weighting
factor which could represent a probability that WSD j is
transmitting. If such a probability is low then the effect on
n.sub.i should also be low.
[0045] An alternative to maximizing the sum-capacity according to
equation (7) is to maximize the secondary sum-power:
f ( p ) = i = 1 N p i . ( 9 ) ##EQU00003##
[0046] A further alternative is to maximize the total WSD
throughput, provided appropriate models are available. E.g., if the
throughput model for the ith WSD may be described as f.sub.i(p),
where the function f.sub.i(p) returns the bits per second, then the
function to maximize becomes:
f ( p ) = i = 1 N f i ( p ) . ( 10 ) ##EQU00004##
[0047] An advantage of embodiments is thus that there is a
flexibility with regards to the choice of objective function to
optimize.
[0048] The Approximation
[0049] The probabilistic interference constraint in (3) is not
straightforward to solve. Particularly, when the components of
G(.alpha.) have a lognormal distribution the weighted sum of these
components has a distribution for which no known expression exists.
In this subsection an efficient approximation is derived.
[0050] There exist several numerical approximations where the sum
of lognormally distributed variables is approximated with another
lognormal variable. Herein, one of these are proposed to be used,
namely the Fenton-Wilkinson (FW) approximation. The reasons for
choosing the FW approximations are twofold: [0051] (a) It is easily
obtainable in closed form which makes it suitable for numerical
optimization; and [0052] (b) It is known to offer a good
approximation for the right tail of the lognormal distribution
(i.e., large values, compared to the medium or median of the
distribution) which is highly relevant for the problem at hand,
since .epsilon. in (3) typically has a low value.
[0053] With the FW approximation, the total interference component
from (3) is rewritten in exponential form:
I tot ( .alpha. , p ) = i = 1 N p i G i ( .alpha. ) I i ( .alpha. ,
p ) = i = 1 N Y i ( .alpha. , p ) .apprxeq. Z ( .alpha. , p ) ( 11
) ##EQU00005##
[0054] where Y.sub.i.about.N(m.sub.yi, .sigma..sub.yi.sup.2),
Z.about.N(m.sub.z, .sigma..sub.z.sup.2) with
m z = 2 ln u 1 - 1 2 ln u 2 ##EQU00006## .sigma. z 2 = ln u 2 - 2
ln u 1 . ##EQU00006.2##
[0055] Furthermore,
u 1 = i = 1 N m y i + .sigma. y i 2 / 2 ##EQU00007## u 2 = i = 1 N
2 m y i + 2 .sigma. y i 2 + 2 i = 1 N - 1 j = i + 1 N m y i + m y i
.rho. i , j ##EQU00007.2## with ##EQU00007.3## .rho. i , j = 1 2 (
.sigma. y i 2 + .sigma. y j 2 + 2 r ij .sigma. y i .sigma. y j )
##EQU00007.4##
[0056] where r.sub.ij denotes the correlation coefficient between
the fading on the signal from WSD i and j:
r ij = E { ( Y i - m y i ) ( Y j - m y i ) } .sigma. y i .sigma. y
j . ##EQU00008##
[0057] By expressing l.sub.i(.alpha.,p) in dB scale, i.e.
l.sub.i,dB(.alpha.,p)=10 log.sub.10 p.sub.i+10 log.sub.10
G.sub.i(.alpha.) the following is obtained:
Y i .about. ( ln p i + ln 10 10 m G i , dB ( .alpha. ) m y i , ( ln
10 10 ) 2 .sigma. G i , dB 3 .sigma. y i 2 ) . ##EQU00009##
[0058] By using the above expressions the distribution of Z which
approximates the log-sum in (11) is defined and may be used to
efficiently approximate the probability constraint in (3).
[0059] Solving the Optimization Problem
[0060] With the above approximations and disregarding any
additional constraints to equation (2), the modified optimization
problem becomes
p=argmax.sub.pf(p,g,n) (12)
[0061] subject to the following constraints:
[max.sub..alpha.Pr{e.sup.Z(.alpha.,p).gtoreq..tau.}].ltoreq..epsilon.
(13)
p.sub.i.gtoreq.0,i=1, . . . ,N (14)
p.sub.i.ltoreq.p.sub.i.sup.max,i=1, . . . ,N (15)
[0062] Further constraints than the ones mentioned in (13)-(15) may
be added. The objective function or utility function may be the sum
capacity which is expressed as:
f(p,g,n)=.SIGMA..sub.i=1.sup.NB log.sub.2
[1+10.sup.(p.sup.i,dBm.sup.+g.sup.i,dB.sup.-n.sup.i,dBm.sup.)/10]
[0063] when the involved quantities are expressed in dB scale (see
(7)).
[0064] In many situations it is not straightforward to know what
value of a that should be used for the probability constraint,
i.e., for which .alpha. the probability of harmful interference is
the largest. In such situations, and potentially also for a
stability of the numerical solver of (12) subject to the
constraints in (13)-(15), the constraint may be solved for a fine
enough grid of .alpha., {.alpha..sub.j}, j=1, . . . , J effectively
replacing the probabilistic constraint in (13) by the analytically
equivalent:
Pr{e.sup.Z(.alpha..sup.j.sup.,p).gtoreq..tau.}.ltoreq..epsilon.,j=1,
. . . J.
[0065] For numerical reasons it is advantageous to operate in the
dB domain. The numerical solver of (12) can also benefit from
knowledge of the gradients of the function f(p) and of the
probability constraint with respect to the power vector in dBm.
These are rather straightforward although tedious to compute and
are described in a paragraph hereinafter. The following parameters
are expected to be supplied to the method by the user: m.sub.Gi,dB,
.sigma..sub.Gi,dB.sup.2, r.sub.ij, .epsilon., .tau., g.sub.i,dB,
n.sub.i,dBm. The inter-WSD parameters g.sub.i,dB, n.sub.i,dBm are
not necessarily known, unless supplied by the WSD. If they are not
known typical values can be used instead.
[0066] Once the modified optimization problem in (12) subject to
constraints (13)-(15) has been solved with a numerical solver, MC
simulations may be used to assert that the probability constraint
is fulfilled. If the constraint is violated or if the solution is
not tight enough the solution can be used as a starting value for
further possibly more complex numerical optimization, or the power
limits from the solution can be given some simple modification. As
an example, the output power limits may increase (if the constraint
(13) is fulfilled with a "too high" margin) or decrease (if the
constraint (13) is not fulfilled) in the direction of the
constraint gradient until the constraint fulfillment is
satisfactory. In this manner output power limits for secondary
units subject to a probabilistic constraint on the aggregate
interference are obtained.
[0067] Alternatively, the optimization can be rerun with a lower
value of .epsilon. or .tau., or initially a lower value than what
the regulators require for .epsilon. or .tau. may be used to
further decrease the probability that harmful interference is
caused.
[0068] Extension to Multiple Channels
[0069] The problems in (2)-(5), and in (12)-(15) make it possible
to control the interference from white space units on a single
channel only. However, WSD transmitters operating on one channel
will typically leak power into neighboring channels, and primary
users operating on neighboring channels will typically have
imperfect receivers which also receive power on other channels than
the operating channel. To this end it may be valuable to control
also the aggregate interference on other channels.
[0070] It is straightforward to extend the problems in (2)-(5), and
in (12)-(15) to take other channels into account. All that needs to
be done is to extend the gain vector G(.alpha.) to a gain matrix
G(.alpha.) where each column represents the gain on a separate
channel, also taking the adjacent channel suppression into account.
For neighboring channels, this would typically include pathloss,
antenna gains, and adjacent channel suppression from the WSD
transmitter. The extended problem in (2)-(5) would look like:
p=argmax.sub.pf(p)
[0071] subject to the following constraints:
[max.sub..alpha.Pr{p.sup.T
G(.alpha.).gtoreq..tau.}].ltoreq..epsilon.
p.sub.i.gtoreq.0,i=1, . . . ,N
p.sub.i.ltoreq.p.sub.i.sup.max,i=1, . . . ,N
[0072] where .tau. now is a row vector. Further constraints than
the ones mentioned here may be added. The probabilistic constraint
may be efficiently approximated using the FW approximation as
described above. In this formulation of the optimization problem
the channels that the WSDs or white space systems use are fixed,
although they need not all use the same channel. A change of
channels would be modeled as a change in G(.alpha.) which is fixed
in the optimization. It should be noted that depending on the areas
to be protected on the other channels, .alpha. may potentially no
longer be interpreted as an angle describing a point on a
protection contour. Checking the constraint along a protection
contour may no longer be sufficient, as it may be so that a larger
area needs to be protected, or that different areas needs to be
protected for each channel, one for each considered channel.
.alpha. will then typically carry an index corresponding to the
area or contour that needs to be protected for the channel
indicated by the index.
[0073] Extension to Include Channel Selection
[0074] Yet another possible extension of the problem and its
efficient approximation taking several channels into account is to
allow the secondary transmitters to transmit on different and
possibly multiple channels. We will denote this "channel
selection", meaning that a channel is selected if a WSD transmits
on it with a non-zero power. M indicates the number of channels and
N indicates the number of WSDs considered. By letting p.sub.ij
denote the power of the ith WSD's transmission on channel j and
letting {tilde over (G)}.sub.ijk(.alpha.) denote the gain on
channel k for the ith WSD's transmission on channel j to the
position described by .alpha., the following is obtained:
p=argmax.sub.pf(p)
[0075] subject to the following constraints:
[ max .alpha. Pr { i = 1 N j = 1 M p ij G ~ ijk ( .alpha. )
.gtoreq. .tau. k } ] .ltoreq. k ##EQU00010## k = 1 , , M
##EQU00010.2## p ij .gtoreq. 0 , i = 1 , , N , j = 1 , , M
##EQU00010.3## p ij .ltoreq. p ij max , i = 1 , , N , j = 1 , , M
##EQU00010.4##
[0076] Further constraints than the ones mentioned here may be
added. When j.noteq.k the gain {tilde over (G)}.sub.ijk(.alpha.)
according to the above also covers leakage onto another channel.
Here .epsilon..sub.k is the acceptable probability of interference
for channel k. The probabilities may be different for different
channels. Typically additional constraints related to the
capabilities of the WSDs need to be added. E.g., the ith WSD may
only be able to transmit on L channels simultaneously and this
would be reflected by adding the constraint
j = 1 M S ( p ij ) .ltoreq. L ##EQU00011##
where S(a) is a step function which is 0 if a.ltoreq.0 and 1
otherwise. Yet another constraint is to require that each WSD has
an upper limit on its total transmit power, i.e., summed over all
channels,
j = 1 M p ij .ltoreq. P i tot , max , i = 1 , , N .
##EQU00012##
The upper limit may be individual, i.e. WSD specific, and may be
dependent on the WSD hardware. Then this constraint may, but does
not necessarily, replace the constraint that
p.sub.ij.ltoreq.P.sub.ij.sup.max, i=1, . . . , N, j=1, . . . M.
Other constraints for which the mathematical formulations are
straightforward to derive are constraints which require that the
secondary transmitter use contiguous channels.
[0077] An advantage of the above mentioned embodiments is thus that
multiple channels may be considered, both when it comes to studying
interference to other frequency channels and when it comes to
selecting the appropriate frequency channels for the WSDs.
Interference to other channels can be an important parameter when
deciding the white space channel availability.
[0078] Other Extensions
[0079] Some of the WSDs may require a minimum power limit in order
to want to use the spectrum. I.e., they may want to have a power of
at least p.sub.i,min, and if they cannot get at least that output
power they may equally use zero power. This may either be handled
by introducing a constraint directly in the above optimization
problem, i.e., replacing the constraint p.sub.i.gtoreq.0 by:
p.sub.i.gtoreq.p.sub.i,min or p.sub.i=0.
[0080] Alternatively, and perhaps more efficiently, it may be
handled in the following manner: [0081] 1. The optimization problem
is solved with the normal p.sub.i.gtoreq.0 constraint. [0082] 2. If
all WSDs get at least their minimum power, then a solution has been
found and the following steps are not needed. [0083] 3. If at least
one WSD has obtained a power limit below its p.sub.i,min, then
remove at least one of these at least one WSDs from the
optimization problem and go back to 1. The WSD(s) which is/are
removed, i.e., which will not be allowed to use the spectrum for
some time, may be arbitrarily selected, or the selection may be
based on other factors such as earlier spectrum usage, device or
service type, relation to the entity allocating the power limits,
or the value of p.sub.i,min. A WSD which used the spectrum
extensively previously may have to cease its transmissions for a
while, or a WSD that is not of a certain type, or does not belong
to a preferred customer may be the first to be removed. In the case
that no WSDs remain after WSD removal, then the requirements of the
WSDs are too high and no secondary spectrum usage is allowed.
[0084] Execution of the Method
[0085] The method described in the previous sections would
typically be executed by a white space database operator (WSDO),
e.g., a white space database operator which is responsible for
controlling the operation of secondary transmitters in the spectrum
such as a geo-location database operator. It should be realized
that a WSDO could also be a single base station controlling
aggregate interference from multiple UEs that it controls, or a
node in a cellular system that controls the aggregate interference
from multiple cells, or an inter cellular system node that controls
the aggregate interference from multiple cells of multiple cellular
systems, or a unit which controls the aggregate interference from
multiple transmitters of various sorts that access the white
space.
[0086] The method would typically execute as follows: [0087] 1.
WSDs report their interest in using spectrum to the WSDO, by
sending a request for usage of the spectrum. They additionally
report information to the WSDO such as WSD positions and output
power limitations, e.g. together with the request. This information
may be used in the optimization in the next step. [0088] 2. The
WSDO uses the input from the WSDs to compute the quantities used in
the optimization problem, as described above. E.g., the gain
vectors G(.alpha.) or the gain matrices G(.alpha.), are computed
using appropriate propagation models and the WSD position
information. Once all relevant quantities are decided, the WSDO
solves the optimization problem as described above in e.g. equation
(12) with constraints in (13)-(15) to obtain the WSDs' output power
limits. [0089] 3. The WSDO informs the WSDs of their respective
output power limits which are the solution to the optimization in
step 2. These output power limits may be valid for some defined
period of time. When this period expires, the WSDs which are
interested in using the spectrum for a next period of time may
repeat the procedure starting in step 1. Alternatively, the period
of time for which the determined output power limits are valid is
not a fixed time period, but may be adapted dependent on the
mobility of the WSDs and dependent on if any new WSDs request to
use the spectrum.
[0090] Numerical Validation
[0091] In this section it is shown that the approximated
optimization problem in (12) subject to the constraints in
(13)-(15) solves well and provides good approximate solutions to
the initial optimization problem in (2) subject to the constraints
in (3)-(5). The validation is made for a single channel. Other
simulations with other parameter settings have been run with
similarly good results.
[0092] The method is validated for an example in which five WSDs
301 are given random positions outside the protection contour 302
of a DTV system. For the probability constraint the variables
.tau.=-100 dBm and .epsilon.=0.5% are used. An example realization
of their positions is given in FIG. 3. The dotted line 303
indicates an average distance from the protection contour of the
randomly generated WSD positions.
[0093] For this realization, median values, i.e., without fading,
of the aggregated interference along the protection contour 403 and
also the interference contribution from each of the individual
transmitters 404 after optimization are shown in FIG. 4. The top
dotted line 401 indicates the threshold .tau.=-100 dBm for harmful
interference and the lower dotted line 402 indicates the threshold
for a single interferer with a fading margin included such that the
probability of harmful interference becomes exactly .epsilon.=0.5%
for the assumed lognormal fading standard deviation .sigma.=7 dB.
Note that each individual interferer needs to keep its power level
below the level which it could use if it were the only transmitter
present. Also note that the median aggregated interference 403 can
exceed the threshold of a single interferer. The reason for this is
that the shadow fading variance of the aggregated interference
becomes lower than that from a single interferer due to averaging.
For this specific realization the FW approximation estimated the
probability of harmful interference to 0.499972% and the actual
probability of harmful interference obtained from MC simulation was
0.4262%.
[0094] From the same realization and solution, the distribution
based on the random fading of the actual received power obtained by
MC simulation and the corresponding FW approximation at the point
on the protection contour which is subject to the highest level of
median interference is plotted in FIG. 5. As can be seen, the FW
approximation is poor for low values of the received power but good
for the upper tail of the interference distribution. This is
consistent with the findings by others and is a desirable behaviour
for the problem at hand.
[0095] Finally, some statistical evaluations are shown. One
thousand realizations of transmitter positions are generated, the
optimization problem in (12) subject to the constraints in
(13)-(15) is solved, and each solution is checked by means of MC
simulations. The optimization software used (Matlab r2009b) is able
to find solutions which very tightly fulfil the probability
constraint. This is due to the fact that both the constraint and
the objective function do not exhibit many local minima.
[0096] FIG. 6 and FIG. 7 show scaled histograms of the actual
probabilities of harmful interference for the solutions to (12), as
computed by MC simulation. FIG. 6 shows the histograms for the
solutions to the one thousand WSD position realizations for shadow
fading standard deviation .sigma.=7 dB, and FIG. 7 shows the
histograms for the solutions to the one thousand WSD position
realizations for shadow fading standard deviation .sigma.=12 dB. It
may be noted that in almost all cases the probability of harmful
interference is slightly underestimated by the FW approximation,
which estimated 0.5%. The underestimation is a good property, as it
is better to be slightly conservative in the power limit decision.
Furthermore, the probabilities of harmful interference are
typically above 0.4%, i.e., close to the desired limit of 0.5%.
This means that the performance of the approximation is very good
for the studied cases.
[0097] The Gradients of the Objective Function and Probability
Constraint
[0098] Here the expressions of the gradients supplied to the
numerical solver of the optimization problem in (12) subject to the
constraints in (13)-(15) are derived.
.delta. f ( p , g , n ) .delta. p i , dBm = B 10 ( p i , dBm + g i
, dB - n i , dBm ) / 10 ln 10 10 ( 1 + 10 ( p i , dBm + g i , dB -
n i , dBm ) / 10 ) ln 2 ##EQU00013##
[0099] and since e.sup.Z(.alpha.,p) is lognormal:
Pr ( e Z ( p ) > .tau. ) = ccdf ( .tau. , p ) = 1 2 - 1 2 erf [
ln .tau. - m z ( p ) 2 .sigma. z 2 ( p ) ] ##EQU00014##
[0100] where erf is the error function. The dependency on .alpha.
is not expressed for notational convenience. Taking the gradient
with respect to p.sub.dBm gives
.differential. ccdf ( .tau. , p ) .differential. p dBm = 1 .pi. exp
[ - ( ln .tau. - m z ( p ) 2 .sigma. z 2 ( p ) ) 2 ] 1 2 .sigma. z
2 ( p ) [ ln .tau. - m z ( p ) 2 .sigma. z 2 ( p ) .differential.
.sigma. z 2 ( p ) .differential. p dBm + .differential. m z ( p )
.differential. p dBm ] ##EQU00015## where ##EQU00015.2## .delta. m
z ( p ) .delta. p dBm = 2 u 1 ( p ) .delta. u 1 ( p ) .delta. p dBm
- 0.5 u 2 ( p ) .delta. u 2 ( p ) .delta. p dBm ##EQU00015.3## and
##EQU00015.4## .delta..sigma. z 2 ( p ) .delta. p dBm = 1 u 2 ( p )
.delta. u 2 ( p ) .delta. p dBm - 2 u 1 ( p ) .delta. u 1 ( p )
.delta. p dBm . ##EQU00015.5##
[0101] There is also
.delta. u 1 ( p ) .delta. p dBm = [ .delta. m y 1 ( p 1 ) .delta. p
1 , dBm exp [ m y 1 ( p 1 ) + .sigma. y 1 2 2 ] .delta. m y N ( p N
) .delta. p N , dBm exp [ m y N ( p N ) + .sigma. y N 2 2 ] ]
##EQU00016## where ##EQU00016.2## .delta. m y i ( p i ) .delta. p i
, dBm = ln 10 10 ##EQU00016.3## and ##EQU00016.4## .differential. u
2 ( p ) .differential. p dBm = [ 2 .differential. m y 1 ( p 1 )
.differential. p 1 , dBm 2 m y 1 ( p 1 ) + 2 .sigma. y 1 2 + 2 j =
2 N .differential. m y 1 ( p 1 ) .differential. p 1 , dBm m y 1 ( p
1 ) + m y j ( p j ) .rho. 1 j 2 .differential. m y 2 ( p 2 )
.differential. p 2 , dBm 2 m y 2 ( p 2 ) + 2 .sigma. y 2 2 + 2 j =
1 j .noteq. 2 N .differential. m y 2 ( p 2 ) .differential. p 2 ,
dBm m y 2 ( p 2 ) + m y j ( p j ) .rho. 2 j 2 .differential. m y N
( p N ) .differential. p N dBm 2 m y N ( p N ) + 2 .sigma. y N 2 +
2 j = 1 N - 1 .differential. m y N ( p N ) .differential. p N dBm m
y N ( p N ) + m y j ( p j ) .rho. N j ] . ##EQU00016.5##
[0102] By combining the above equations the gradients are readily
available.
[0103] Method and Node
[0104] FIG. 8a is a flowchart of a method of a node for controlling
an aggregated interference generated by at least two white space
units in at least one point in space for at least one frequency
channel, according to embodiments. The at least one point in space
may in embodiments correspond to a point, a line, an area, or a
volume. Each of the at least two white space units may be a WSD, or
a white space system. In one embodiment the node is a geo-location
database. A model of propagation channels from each of the at least
two white space units to each of the at least one point comprises a
variable with a lognormal distribution. The method comprises:
[0105] 810: Receiving requests for usage of white space frequency
channels from the at least two white space units. The requests
comprises positions of the at least two white space units. In one
example embodiment, a request for usage of white space frequency
channels is received from each one of two WSDs, and each request
comprises the position of the requesting WSD. In another example
embodiment, a white space system may determine what positions its
WSDs have and transmit the positions in the request to the node.
Such a position is understood to be information relating to a
geographical position of a white space unit. This position may be
either a precisely defined point in space, or less specific
information including uncertainty. Position uncertainty may be
described by defining a probability distribution over a
geographical area or volume, e.g., a uniform distribution over a
disk as illustrated in FIG. 2, and may be treated by assuming that
the position in each case is the worst-case position, i.e., the
allowed position closest to the protection contour. [0106] 820:
Determining output power limits for the at least two white space
units by maximizing a utility function while fulfilling a
probabilistic constraint on the amount of aggregated interference
generated in each of the at least one point, based on the received
requests and on said model of propagation channels. A sum of
lognormal variables in the probabilistic constraint is approximated
by a single lognormal variable. In one embodiment a FW
approximation is used for approximating the sum of lognormal
variables by a single lognormal variable, as previously described
in the section "The approximation" above. The utility function,
also called the objective function above, may in embodiments be one
of a sum-capacity; a sum-power; or a total throughput of the at
least two white space units. The probabilistic constraint may
correspond to a probability that each of the at least one points
has an aggregated interference which exceeds an interference value
threshold, wherein the probability is constrained to be below a
probability threshold. In one embodiment, the probabilistic
constraint corresponds to the constraint that none of the at least
one points have a greater probability than .epsilon. of having an
aggregated interference which exceeds an interference value
threshold .tau.. .epsilon. and .tau. may typically be set by a
regulator. A probabilistic constraint is given in constraint (3)
above. [0107] 830: Transmitting the determined output power limits
to the respective at least two white space units. In response to
the white space units' request for white space channels, the white
space units receive output power limits in a reply from the node
controlling the interference. The white space units may thus start
using the white space that they have been allocated, taking care
not to exceed the output power limits that they have received from
the node.
[0108] FIG. 8b is a flowchart of the method according to another
embodiment, previously described in the section "Solving the
optimization problem" above. The method further comprises after
steps 810 and 820 described above: [0109] 825: Checking by means of
an MC simulation if the determined output power limits fulfil the
probability constraint. [0110] 830: Transmitting the determined
output power limits to the respective at least two white space
units if the determined output power limits fulfil the probability
constraint.
[0111] As already mentioned above, the determining of output power
limits may in embodiments be subject to additional constraints. In
one embodiment, the determining of output power limits is subject
to an additional constraint that the determined output power limits
must be equal to or lower than a maximum output power value. This
constraint corresponds to the constraint in (5) above. The maximum
output power value may be received in at least one of the requests.
This may e.g. be the case when the white space unit have no use of
a power level higher than the maximum output power level, and
therefore provides the value in its request. Alternatively it may
be pre-defined, or it may be determined based on capabilities of
the at least two white space units. In one embodiment, the maximum
output power value may be transmitted implicitly by e.g.
transmitting an indication of what WSD class that the WSDs belong
to, which determines what maximum output power that the WSDs may
use.
[0112] In a further embodiment the determining of output power
limits is subject to an additional constraint that the determined
output power limits must be the same for all of the at least two
white space units. This constraint corresponds to the power
fairness constraint described previously.
[0113] In one embodiment, which may be combined with any of the
previously described embodiments, the method further comprises
comparing one or more of the determined output power limits with a
minimum output power value related to a corresponding white space
unit. If at least one of the determined output power limits is
below the minimum output power value, the method comprises
determining the output power limits again with at least one of the
at least two white space units removed. The minimum output power
value may be received in at least one of the requests. This
embodiment is further described in the section "Other extensions"
above.
[0114] In still another embodiment, further described in the
section "Extension to multiple channels" above, the aggregated
interference is controlled in at least two frequency channels, and
the model of propagation channels for the at least two frequency
channels takes adjacent channel suppression into account.
[0115] In one embodiment, further described in the section
"Extension to include channel selection" above, the maximizing of
the utility function comprises a selection of at least one of
several frequency channels for each of the at least two white space
units. The determining of output power limits may in this first
embodiment be subject to at least one of the following constraints:
a constraint on a number of simultaneously used frequency channels
for the at least two white space units; a constraint on a total
transmit power for each of the at least two white space units over
all selected frequency channels; a constraint that the at least two
white space units must use contiguous frequency channels.
[0116] A node 900 and a white space unit 950 are schematically
illustrated in FIG. 9a according to embodiments. The node is in one
embodiment a geo-location database. The node 900 is configured to
control an aggregated interference generated by at least two white
space units in at least one point in space for at least one
frequency channel. A model of propagation channels from each of the
at least two white space units to each of the at least one point
comprises a variable with a lognormal distribution. The node
comprises a communication unit 920 and a processing unit 910,
wherein the communication unit 920 is configured to receive
requests for usage of white space frequency channels from the at
least two white space units, the requests comprising positions of
the at least two white space units. The processing unit 910 is
configured to determine output power limits for the at least two
white space units by maximizing a utility function while fulfilling
a probabilistic constraint on the amount of aggregated interference
generated in each of the at least one point, based on the received
requests and on said model of propagation channels. A sum of
lognormal variables in the probabilistic constraint is approximated
by a single lognormal variable. The communication unit 920 is
further configured to transmit the determined output power limits
to the respective at least two white space units.
[0117] In embodiments, the processing unit 910 is further
configured to check by means of an MC simulation if the determined
output power limits fulfil the probability constraint, and the
communication unit 920 is further configured to transmit the
determined output power limits to the respective at least two white
space units if the determined output power limits fulfil the
probability constraint.
[0118] In still another embodiment, the processing unit is
configured to approximate the sum of lognormal variables by a
single lognormal variable by using a FW approximation.
[0119] In another embodiment, the processing unit is configured to
determine output power limits subject to an additional constraint
that the determined output power limits must be equal to or lower
than a maximum output power value.
[0120] The processing unit may be configured to determine output
power limits subject to an additional constraint that the
determined output power limits must be the same for all of the at
least two white space units.
[0121] In one embodiment, the processing unit is further configured
to compare at least one of the determined output power limits with
a minimum output power value related to a corresponding white space
unit, and to determine the output power limits again with at least
one of the at least two white space units removed, if the at least
one of the determined output power limits is below the minimum
output power value. The communicating unit may be configured to
receive the minimum output power value in at least one of the
requests.
[0122] In one embodiment, the maximizing of the utility function
comprises a selection of at least one of several frequency channels
for each of the at least two white space units. The processing unit
may then optionally be configured to determine output power limits
subject to at least one of the following constraints: a constraint
on a number of simultaneously used frequency channels for the at
least two white space units; a constraint on a total transmit power
for each of the at least two white space units over all selected
frequency channels; a constraint that the at least two white space
units must use contiguous frequency channels.
[0123] The units described above with reference to FIG. 9a may be
logical units or separate physical units, or a combination of both
logical and physical units.
[0124] FIG. 9b schematically illustrates an embodiment of the node
900, which is an alternative way of disclosing the embodiment
illustrated in FIG. 9a. The node 900 comprises a Central Processing
Unit (CPU) 970 which may be a single unit or a plurality of units,
and the communication unit 920 already described above.
Furthermore, the node 900 comprises at least one computer program
product 975 in the form of a non-volatile memory, e.g. an EEPROM
(Electrically Erasable Programmable Read-Only Memory), a flash
memory or a disk drive. The computer program product 975 comprises
a computer program 976, which comprises code means which when run
on the node 900 causes the CPU 970 on the node 900 to perform the
steps of the method described earlier in conjunction with FIGS. 8a
and 8b.
[0125] Hence in the embodiments described, the code means in the
computer program 976 of the node 900 comprises a module 976a for
determining output power limits for the at least two white space
units. It also comprises a module 976b for checking by means of an
MC simulation if the determined output power limits fulfil the
probability constraint. The code means may thus be implemented as
computer program code structured in computer program modules. The
modules 976a-b essentially perform the steps 820 and 825 of the
flow in FIGS. 8a and 8b to emulate the node described in FIG. 9a.
In other words, when the different modules 976a-b are run on the
CPU 970, they correspond to the unit 910 of FIG. 9a.
[0126] Although the code means in the embodiment disclosed above in
conjunction with FIG. 9b are implemented as computer program
modules which when run on the node 900 causes the node to perform
the steps described above in conjunction with FIGS. 8a and 8b, one
or more of the code means may in alternative embodiments be
implemented at least partly as hardware circuits.
[0127] The above mentioned and described embodiments are only given
as examples and should not be limiting. Other solutions, uses,
objectives, and functions within the scope of the accompanying
patent claims may be possible.
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